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Categories for the Practising Physicist | Enteropia
https://enteropia.wordpress.com/2011/12/10/categories-for-the-practising-physicist
The bright side of me. Number of Inversions: Image vs. Text. Why Does a Tiger Have Stripes and a Lion Doesn’t? Categories for the Practising Physicist. December 10, 2011. These days I’m reading and trying to understand “Categories for the practising physicist”. By Bob Coecke and Eric Oliver Paquette, the chapter from the book “New Structures for Physics”. Another its chapter — “Physics, Topology, Logic and Computation: A Rosetta Stone”. By John Baez and Mike Stay — is quite famous among haskellers. Which...
Rubber and Rubber Balloons: Paradigms of Thermodynamics | Enteropia
https://enteropia.wordpress.com/2013/03/31/rubber-and-rubber-balloons-paradigms-of-thermodynamics
The bright side of me. Rubber and Rubber Balloons: Paradigms of Thermodynamics. March 31, 2013. I have just finished reading a book “Rubber and Rubber Balloons: Paradigms of Thermodynamics”. By Ingo Müller and Peter Strehlow. For the details I refer you to the book. Apart from rubber balloons, which are no doubt fun, the rubber itself is a very interesting material. It were its remarkable properties which made me at last find some time and read a book about rubber. This entry was posted in Physics. Fill ...
Why Does a Tiger Have Stripes and a Lion Doesn’t? | Enteropia
https://enteropia.wordpress.com/2011/12/18/why-does-a-tiger-have-stripes-and-a-lion-doesnt
The bright side of me. Categories for the Practising Physicist. Why Does a Tiger Have Stripes and a Lion Doesn’t? December 18, 2011. I’ve encountered a pretty nice insult on reductionism in the “Categories for the Practising Physicist”. I’ll just cite the whole. Why does a tiger have stripes and a lion doesn’t? One might expect that the explanation is written within the fundamental building. This example illustrates how monoidal categories enable to shift the focus from an. In my opinion the reasoning ab...
ASCII-art Math | Enteropia
https://enteropia.wordpress.com/2012/06/09/ascii-art-math
The bright side of me. Rubber and Rubber Balloons: Paradigms of Thermodynamics →. June 9, 2012. Many of computer algebra systems date back to the times when GUI machines were rare and expensive, if were present at all. Thus command line was a standard interface. Unfortunately text terminal doesn’t fit very well for displaying mathematical expressions which demand for rich typesetting. To represent math formulas CAS’s resorted to some kind of ASCII art:. That’s the output of Maxima. I’ve tried to en...
Yrogirg | Enteropia
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The bright side of me. Rubber and Rubber Balloons: Paradigms of Thermodynamics. March 31, 2013. I have just finished reading a book “Rubber and Rubber Balloons: Paradigms of Thermodynamics” by Ingo Müller and Peter Strehlow. It is a nice easy-going undergrad reading exploring rubber and its properties from a thermodynamic point of view. The authors … Continue reading →. June 9, 2012. January 29, 2012. I have nothing to write :-) But I will write! Why Does a Tiger Have Stripes and a Lion Doesn’t? These da...
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thestandinginvitation.wordpress.com
Things That Don’t Look Like Anything | The Standing Invitation
https://thestandinginvitation.wordpress.com/2012/03/26/things-that-dont-look-like-anything
Things That Don’t Look Like Anything. The thought makes people uncomfortable. The idea of something not looking like anything is not a new one. Sounds do not look like anything. We know that sounds exist, but that physical appearance is not something we can ascribe to them. When we talk about sounds, we describe them in nonvisual terms. Sounds, or ideas or desires or smells, have a certain abstract quality that seems to excuse this. But particles are. But what about objects that are even smaller? The mic...
L’Hopital’s Rule for Limits | My Math Blog
https://pqnelson.wordpress.com/2012/06/13/lhopitals-rule-for-limits
A topnotch WordPress.com site. Series Convergence: What Does It Mean? L’Hopital’s Rule for Limits. June 13, 2012. Now we are concerned about limits and we can have nightmarish limits. For example if. What can we do? We end up using derivatives to help evaluate such limits. We have L’Hopital’s rule state, if. 2 Sketch of Proof. We can use linear approximations. Use these approximations in (1a), then take the limit. So our limit becomes. We evaluate the inner limit first. So (4) simplifies to. You are comm...
Inverse Function Theorem | My Math Blog
https://pqnelson.wordpress.com/2012/06/04/inverse-function-theorem
A topnotch WordPress.com site. Optimization (Motivation) →. June 4, 2012. So we have some function. The “Inverse Function”. Is another function denoted. Be a function of. So what happens if we differentiate both sides of Equation (1) with respect to. The right hand side is trivial. The left hand side is more interesting. We see, by the chain rule, it is. But we do not know how to differentiate an inverse function…what to do? Why not set Equations (2) and (3) equal? Be a function and. What do we do? Pingb...
Antidifferentiation (Part 1) | My Math Blog
https://pqnelson.wordpress.com/2012/06/06/antidifferentiation-part-1
A topnotch WordPress.com site. Endomorphisms of the Fano Plane. Antidifferentiation (Part 2: Indefinite Integration) →. June 6, 2012. 1 Derivatives Properties Review. Be given. We recall the derivative. We have several rules for differentiation:. We want to introduce an “inverse” of differentiation. We will use the notation. Is an “Antiderivative”. Usually it’s an open interval) iff. What is its antiderivative? Well, we see its of the form. We take its derivative. To be equal to. Is the antiderivative for.
Exponential Function | My Math Blog
https://pqnelson.wordpress.com/2012/06/03/exponential-function
A topnotch WordPress.com site. Line Tangent to a Curve. Tangent Lines as Linear Approximations →. June 3, 2012. So we threw down a challenge at the end of our discussion of Tangent Lines. Recall we wanted to find a curve. Such that for any. We have the line tangent to that point. Historical note: Debeaune asked Descartes this problem in a letter in 1638; Leibniz solved this problem in 1684 using “infinitesimals”. We will use modern calculus to solve the problem! We can rewrite this to be. We could do this.
Implicit Differentiation | My Math Blog
https://pqnelson.wordpress.com/2012/06/04/implicit-differentiation
A topnotch WordPress.com site. Future Directions (After Differential Calculus) →. June 4, 2012. Recall a circle consists of the points. Question: how do we construct the line tangent to a point on the circle? This problem really boils down to “How do we take the derivative of Equation (1)? 8221; Since this is the meat of the matter, lets study this problem. What we can try to do is differentiate everything in (1) with respect to. We could then use the chain rule. Then evaluate the derivative to obtain.
Alex Nelson | My Math Blog
https://pqnelson.wordpress.com/author/jbufordjr
A topnotch WordPress.com site. Author Archives: Alex Nelson. I like math. I like programming. Most of all, I love puzzles. Index] Calculus in a Single Variable. October 26, 2013. Just to keep readers in the loop: I have not forsaken you! I just have a job now… I got hired to program in Clojure, a peculiar member of the Java family and distant relation to the LISP clan. Nevertheless, … Continue reading →. September 22, 2012. Introduction to Double Integration. July 25, 2012. Notes on Mathematical Writing.
Optimization Example: Area of Rectangle | My Math Blog
https://pqnelson.wordpress.com/2012/06/04/optimization-example-area-of-rectangle
A topnotch WordPress.com site. First Derivative Test →. Optimization Example: Area of Rectangle. June 4, 2012. We have a string of length. It does not stretch. But we want to form a rectangle using this string as its boundary. Moreover we want this rectangle’s area is maximized. What to do? Spoiler alert: solution below! Well, if we form a rectangle, then it has sides. The perimiter is equal to the length of string). The area would be. This seems simple enough. We impose our constraint to write. Index] C...
[Index] Calculus in a Single Variable | My Math Blog
https://pqnelson.wordpress.com/2013/10/26/index-calculus-in-a-single-variable
A topnotch WordPress.com site. Index] Calculus in a Single Variable. October 26, 2013. Differential Calculus in a Single Variable. Using big O notation. Line Tangent to a Curve. Tangent Lines as Linear Approximations. Some Useful Trigonometric Limits. The inverse function to the exponential mapping. The First Derivative Test. An example optimizing a rectangle’s area. Curve Sketching (General Scheme). L’Hopital’s Rule for Limits. Differentiation Technique #1: Logarithmic Differentiation. You are commentin...
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Enteropia | The bright side of me
The bright side of me. Rubber and Rubber Balloons: Paradigms of Thermodynamics. March 31, 2013. I have just finished reading a book “Rubber and Rubber Balloons: Paradigms of Thermodynamics”. By Ingo Müller and Peter Strehlow. For the details I refer you to the book. Apart from rubber balloons, which are no doubt fun, the rubber itself is a very interesting material. It were its remarkable properties which made me at last find some time and read a book about rubber. June 9, 2012. Many of computer algebra ...
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